Question

when an object is at a distance u1 and u2 from a lens,real image and a virtual image is formed respectively having same magnification.the focal length of the lens is

Answer 1

1/v1 + 1/u1 = 1/f1 ….(1)

When an image is virtual

1/(-v2) + 1/u2 = 1/f ….(2)

From equation (1)

V1 = u1f/ u1 – f

Or,  v1/u1 = f/u1 –f = magnification  (m)

From equation (2)

V2 = u2f/ f –u2

Or, v2/u2 = f/f-u2 = magnification  (m1)

If m = m1

Or,  f/u1 –f = f/f-u2

Or, f = u1 + u2/2 = Focal length